I've been walking on smooth rock exposed because the river is low. When it's wet it's quite slippy. Converse fared okay, even with worn down soles. Didn't trust them though because they can be slippy. Switched to my hiking boots the next day, which have hard rubber Vibram soles. Saw Vibram soles recommended in a couple of places discussing the same thing - they were disastrous in my case. Great for muddy conditions, definitely not suitable for wet smooth rock though.
Boat shoes would seem to make the most sense (if they're designed for purpose and not for style, I'm guessing it might be the latter with most). So I'm thinking fairly flat soft rubber soles might work the best- maybe Converse are a good choice. Basketball courts are similar sorts of surfaces I guess. Fairly short route; just a few km, so support and ruggedness not too big a deal.